# How do you find an equation that describes the sequence #16, 17, 18, 19,...# and find the 23rd term?

##### 2 Answers

#### Explanation:

To find an equation, we should use the **arithmetic sequence** formula:

When using this formula, you need to find the values for

**1. Finding #d# (common difference)**

We are given the sequence **common difference ( #d#),** which is another way of saying the difference between any two consecutive numbers in the arithmetic sequence. You could find

etc.

But whatever way you choose to find it, you should get that

**2. Finding #a_1#**

**3. Plug into the formula**.

Now distribute

That's your equation!

Now plug in 23 for

#### Explanation:

#" this is an arithmetic sequence"#

#"the nth term is " a_n=a+(n-1)d#

#"where " a " is the first term and " d" the common difference"#

#"here " a=16" and " d=1#

#rArra_n=16+n-1=n+15#

#rArra_(23)=23+15=38#